Problem: Solve for $x$ and $y$ using elimination. ${2x-4y = -10}$ ${-2x+5y = 17}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {2x-4y = -10}\thinspace$ to find $x$ ${2x - 4}{(7)}{= -10}$ $2x-28 = -10$ $2x-28{+28} = -10{+28}$ $2x = 18$ $\dfrac{2x}{{2}} = \dfrac{18}{{2}}$ ${x = 9}$ You can also plug ${y = 7}$ into $\thinspace {-2x+5y = 17}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(7)}{= 17}$ ${x = 9}$